Why am I getting a System.ArithmeticException with C#'s Nuget BigInteger 1.0.7?

Question

So, I've been learning C# and testing some simple algorithms out. I made this simple class that exposes a recursive Fibonacci number function. I use memoization (Dynamic Programming) to store previously found numbers. Here's the code:

    using Godot;
    using System.Collections.Generic;

    public class Exercise1 : Node {
      private BigInteger teste = new BigInteger(1);
      private Dictionary<BigInteger,BigInteger> memory = new Dictionary<BigInteger,BigInteger>();
      public override void _Ready() {
        RunBigIntegerCraziness();
      }

    private void RunBigIntegerCraziness() {
      for (int i = 0; i < 31227; i++) {
        GD.Print($"fib number {i} is {fib(new BigInteger(i))}");
      }
    }

    private BigInteger fib(BigInteger n) {
      if (memory.ContainsKey(n)) {
        return memory[n];
      }

      if (n <= 2) {
        memory[n] = 1;
        return 1;
      }

      memory[n - 2] = fib(n - 2);
      memory[n - 1] = fib(n - 1);

      return memory[n - 2] + memory[n - 1];
    }
    }

Ignore the "Godot" part. It's just that I was testing this inside a game project. Everything compiles fine, but I can only calculate up to Fibonacci n. 3226. If I go to numbers equal to 3227 and beyond, I get this Exception:

[...] fib number 3225 is 43217018697618272220345809139733426666656338842625944764401661804465121290773093888861438958973337206110398501101783011185091567135587979099219045977958276652741787987152919489957724618258731270111934419344108965974546742136386635343927537356176338553654798753734888560554135669621772542530920892471422002609630627040146600381068673360870794221630560104764217344676242315795514744073614579107596818134891238017641931792490286597416223216551326908997909707498658766245465906764466010328772845314077258564566442129155001040721886128505146365749238671331993692655687520038382893117763783477305776640877748401894737521738794911907045829607125767696264441933278046913082328818850 fib number 3226 is 69926605145186078778460989556214883682824163521963475389625827936774132010815037784261200216187927277027753726906285824183824754568491676416709800266452379691484582909141867315765704538889919267496081895355700988068705924800720430980434359659981529442293650167261872365958477365094269319478110803029308487644284790516508517647989046631899202985143468253781566270183590285229230335042129126551683888682955813507183937267823895233985645240278207971782178625906849647650415867576295127507836850507509010403410481726883571748090361307264480634218098397060429202475118649538779225621232854604363989464362465170636407301900981359138471646464444082736135056091569488488491377766743

Unhandled Exception: System.ArithmeticException: Overflow or underflow in the arithmetic operation. at BigInteger.op_Addition (BigInteger bi1, BigInteger bi2) [0x000fa] in :0 at Exercise1.fib (BigInteger n) [0x000a8] in /Users/rafael/gamedev/godot/mytests/CSharpStudy/study_classes/Exercise1.cs:31 at Exercise1.RunBigIntegerCraziness () [0x00006] in /Users/rafael/gamedev/godot/mytests/CSharpStudy/study_classes/Exercise1.cs:15 at Exercise1._Ready () [0x00001] in /Users/rafael/gamedev/godot/mytests/CSharpStudy/study_classes/Exercise1.cs:10 The terminal process terminated with exit code: 1

Aren't "BigInteger"s supposed to handle pretty high numbers??

Answer 1

In the source of that BigInteger, there is:

// maximum length of the BigInteger in uint (4 bytes)
// change this to suit the required level of precision.
private const int maxLength = 70;

The length is counted in limbs, each limb is 32 bits in this implementation. Additionally, the topmost bit of the topmost limb is treated as a sign bit. Therefore, without changing the source the maximum number that can be stored in this kind of BigInteger (this limit does not apply to the BigInteger in System.Numerics) is 2^70*32-1-1, or in other words, there are 2239 "normal" bits available.

That allows for some fairly big integers, but not big enough: according to Wolfram Alpha fib(3227) requires just over 2239 bits, therefore it does not fit.